1
GATE ECE 2015 Set 3
Numerical
+1
-0
The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x \right|{e^{ - \left| x \right|}}\,\,$$ is ___________.
2
GATE ECE 2015 Set 2
Numerical
+1
-0
Let the random variable $$X$$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $$X$$ is ________.
3
GATE ECE 2015 Set 2
+1
-0.3
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $$1/6$$ and that of Ramesh is $$1/8$$. What is the probability that only one of them will be selected?
A
$$47/48$$
B
$$1/4$$
C
$$13/48$$
D
$$35/48$$
4
GATE ECE 2015 Set 1
+1
-0.3
Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \right) \ne 0.$$ Let $$\overrightarrow A$$ & $$\overrightarrow B$$ be their complements. Which of the following statements is FALSE?
A
$$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$$
B
$$P\left( {A/B} \right) = P\left( A \right)$$
C
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right)$$
D
$$P\left( {\overrightarrow A \cap \overrightarrow B } \right) = P\left( {\overrightarrow A } \right).P\left( {\overrightarrow B } \right)$$
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
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